retired; previous position (1983-2015): tenured researcher, State Universities of Milan, Milan, IT. (since 2007) Fellow of the Electromagnetics Academy, Cambridge, MA. (1999) visiting scientist, Dept. of Electrical Engineering, University of Massachusetts, Lowell, MA. (1992) short term visitor, Institute for Mathematics and Applications, Minneapolis, MN. (1989) visiting Associate Professor, Dept. of Mathematics, Texas A&M Univ., College Station, TX. (1988) visiting scholar, Dept. of Mathematical Sciences, Univ. of Delaware, Newark, DE. (1975-1983) independent consultant. (1974-1975) tactical control assistant, NATO Hawk anti-aircraft artillery. Author of 65 peer-reviewed articles, 37 editor-reviewed articles, 65 conference abstracts. Presenter of 118 conference talks, 12 conference posters, 62 seminars. Co-editor of 5 special issues and proceedings. Co-author of 1 textbook. Signer of 84 Mathematical Reviews. Research interests: inverse problems for partial differential equations (electromagnetics, acoustics, fluid dynamics), image recognition, materials characterization, morphogenesis. Teaching assignments: (1995 to 2014, University of Milan Bicocca) Mathematical models & methods for the environmental sciences, (2005-2007, same) Dynamics and control of environmental systems, (2007, same) Process control,(1991-1994, University of Milan, IT) Theory of computing machines, (1989, Texas A&M University, College Station, TX) Calculus I, (1981- 1988, University of Milan, IT) Physics II. Advisor or co-advisor of 80 M.Sc. thesis projects Professional association: American Mathematical Society, Applied Computational Electromagnetics Society, Associazione Meccanica VA (hon.), Imaging Science and Technology Society (emeritus), Institute of Electrical and Electronics Engineers (life senior), Materials Research Society, Mathematical Association of America, SPIE. Publications web site: https://boa.unimib.it/browse?type=author&order=ASC&rpp=20&authority=rp04149 (2016 Feb 24)
Publications (24)
This will count as one of your downloads.
You will have access to both the presentation and article (if available).
Data from single-cell mRNA sequencing, made available by leading-edge experimental methods, demand proper representation and understanding. Multivariate statistics and graph theoretic methods represent cells in a suitable feature space, assign to each cell a time label known as “pseudo-time” and display “trajectories” (in fact orbits) in such space. Orbits shall describe a process by which progenitors differentiate into one or more types of adult cells: broncho-alveolar progenitors are e.g., found to evolve into two distinct pneumocyte types. This work aims at applying the qualitative theory of dynamical systems to describe the differentiation process. Some notions of qualitative theory are presented (§ 2). The main stages of single-cell data analysis are outlined (§ 3). Next, a two-dimensional continuous time, autonomous dynamical system of polynomial type is looked for, the orbits of which may interpret some sequences of data points in feature (⌘ state) space. Section 4 defines an energy function F of two variables, 1,!2}, and the autonomous dynamical system obtained from rF, which thus generates a gradient flow. Both F and the gradient flow give rise to a phase portrait with two attractors, A and B, a saddle point, O, and a separatrix. These properties are suggested by data from single cell sequencing. Initial states of the system correspond to progenitors. Attractors A and B correspond to the two cell types yielded by progenitor differentiation. The separatrix and the saddle point make sure an orbit asymptotically reaches either A or B. Why and how a gradient flow model shall be applied to data from single-cell sequencing is discussed in § 5. The application of dynamical system theory presented herewith relies on a heuristic basis, as all population dynamics models do. Nonetheless, placing a given cell on an orbit of its own enables time ordering and compliance with causality, unlike pseudo-time assignment induced by a minimum spanning tree. An earlier (2009) application in a much simpler context, the evolving morphology of cytoskeletal tubulines, is finally recalled: from cyto-toxicity experiments, epifluorescence images of tubulin filaments were obtained, then analysed and assigned to morphology classes; class centroids formed a sequence in feature (⌘ state) space describing loss of cytoskeletal structure followed by its recovery.
Causality and passivity constraints appear in constitutive equations of any material or meta-material and characterise the interaction electromagnetic radiation with matter. These constraints result in the well-known physical limitations which affect the design of a cloak. However, there are items in the realm of partial differential equations, namely transmission eigenvalue problems in electromagnetics, which have ignored such physical limitations and are nonetheless believed to play a role in cloaking theory. Herewith, some properties of elliptic partial differential equations are recalled; the main properties of Maxwell-Herglotz pairs are listed; transmission eigenvalue problems are stated, their connections with the properties of the “far-field scattering” operator and to “nearly non-scattering” solutions are discussed. Finally, results coming from transmission eigenvalue problems of electromagnetics, where material models ignore causality and passivity, are shown to be of limited application to cloaking.
Scattering patterns are made available by the TAOS (Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting micrometer-sized single airborne aerosol particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. TAOS patterns have been classified by a learning machine, the training stage of which depends on many control parameters. Patterns due to single bacterial spores (Bq class) have to be discriminated from those produced by outdoor aerosol particles (Kq set) and diesel soot aggregates (sq set), where both Kq and sq are assumed not to contain patterns of bacterial origin. This work describes two directions along which classification continues to develop: the enlargement of the control parameter set and the simultaneous processing of two areas (sectors) selected from the TAOS pattern. The latter algorithm is meant to make the classifier sensitive to simmetry exhibited by some patterns. The available classification scheme is summarized, as well as the rule by which discrimination is rated off-line. Discrimination based on one pattern sector alone scores fewer than 15% false negatives (misclassified Bq patterns) and false positives from Kq and sq. Discrimination based on the symmetry of two pattern sectors fails to recognize 30% of the Bq (bacterial) patterns, whereas < 5% Kq (environmental) patterns are assigned to the Bq class; false positives from sq (diesel) patterns drop to zero. The issue of false positives is briefly discussed in relation to the fraction of airborne bacteria found in aerosols.
A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential,
q0 induce transformations of the scattered wave. The latter can be represented by means of Born sequences,
where q0 appears under the integral sign: non-local formulas are thus derived, the properties of which are
discussed. Next, the symmetries induced by the 1st BORN approximation are addressed. Invariance of the
squared modulus of the scattering amplitude holds for translation and reflection. The transformation Tε :=
13 +Σ3ℓ=1εℓAℓ, with {εℓ;} real and {Aℓ} the generators of rotations in IR3, is investigated. Conditions on the
{ε ℓ} are derived, by which the scattering amplitude coming from the first BORN approximation is invariant to Tε. As an application, these “false symmetries” are compared to those induced by limited angular resolution
of a detector in light scattering experiments. Namely, scattering patterns are made available by the TAOS
(Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting single airborne aerosol
particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. The
optics and the detector properties determine the resolution at which a pattern is saved. The implications on the
performance of TAOS pattern analysis are briefly discussed.
Two-dimensional angle-resolved optical scattering (TAOS) is an experimental method which collects the intensity pattern of monochromatic light scattered by a single, micron-sized airborne particle. In general, the interpretation of these patterns and the retrieval of the particle refractive index, shape or size alone, are difficult problems. The solution proposed herewith relies on a learning machine (LM): rather than identifying airborne particles from their scattering patterns, TAOS patterns themselves are classified. The LM consists of two interacting modules: a feature extraction module and a linear classifier. Feature extraction relies on spectrum enhancement, which includes the discrete cosine Fourier transform and non-linear operations. Linear classification relies on multivariate statistical analysis. Interaction enables supervised training of the LM. The application described in this article aims at discriminating the TAOS patterns of single bacterial spores (Bacillus subtilis) from patterns of atmospheric aerosol and diesel soot particles. The latter are known to interfere with the detection of bacterial spores. Classification has been applied to a data set with more than 3000 TAOS patterns from various materials. Some classification experiments are described, where the size of training sets has been varied as well as many other parameters which control the classifier. By assuming all training and recognition patterns to come from the respective reference materials only, the most satisfactory classification result corresponds to ≈ 20% false negatives from Bacillus subtilis particles and ≤ 11% false positives from environmental and diesel particles.
Polyethylene terephthalate-alumina nano-composites from two production processes gave rise to materials H and T,
further divided into four and, respectively, three classes of belonging. Electron microscope images of the materials had
been visually scored by an expert in terms of an index, β, aimed at assessing filler dispersion and distribution. These
properties characterize the nano-composite. Herewith a classification algorithm which includes image spatial
differentiation and non-linear filtering interlaced with multivariate statistics is applied to the same images of materials
Hand T. The classification algorithm depends on a few parameters, which are automatically determined by maximizing a
figure of merit in the supervised training stage. The classifier output is a display on the plane of the first two principal
components. By regressing the 1st principal component affinely against β a remarkable agreement is found between
automated classification and visual scoring of material H. The regression result for materialT is not significant, because
the assigned classes reduce from 3 to 2, both by visual and automated scoring. The output from the non-linear image
filter can be related to filler dispersion and distribution.
Two types of tread wear particles are investigated: tread wear particles from a steel brush abrader (TrBP) and particles
produced during a steering pad run (TrSP). A leaching experiment in water at pH = 7.5 for 24 and 48h was carried out on
TrBP to simulate environmental degradation. Images of all materials were collected by a scanning electron microscope
(SEM) together with element microanalytical (EDX) data. Surface morphology is described by a function of wave
number (the "enhanced spectrum") obtained from SEM image analysis and non-linear filtering. A surface roughness
index, ρ, is derived from the enhanced spectrum. The innovative contribution of this work is the representation of
morphology by means of ρ, which, together with EDX data, allows the quantitative characterization of the materials. In
particular, the surface roughness of leached TrBP is shown to decay in time and is related to the corresponding
microanalytical data for the first time. The morphology of steering pad TrSP, affected by included mineral particles, is
shown to be more heterogeneous. Differences in morphology (enhanced spectra and ρ), elemental composition and
surface chemistry of TrBP and TrSP are discussed. All methods described and implemented herewith can be
immediately applied to other types of tread wear material. The arguments put forward herewith should help in the proper
design of those experiments aimed at assessing the impact of tread wear materials on the environment and on human
health.
Two-dimension, angle-resolved optical scattering (TAOS) is an experimental technique by which patterns of LASER
light intensity scattered by single (micrometer or sub-micrometer sized) airborne particles are collected. In the past 10
years TAOS instrumentation has evolved from laboratory prototypes to field-deployable equipment; patterns are
collected by the thousands during indoor or outdoor sampling in short times. Although comparison between
experimental and computed scattering patterns has been carried out extensively, there is no satisfactory way to relate a
given pattern to the particle it comes from. This paper reports about the ongoing development and implementation of a
method which is aimed at classifying patterns, rather than identifying original particles. A machine learning algorithm
includes the extraction of morphological features and their multivariate statistical analysis. A classifier is trained and
validated in a supervised mode, by relying on patterns from known materials. Then the tuned classifier is applied to the
recognition of patterns of unknown origin.
For a long time acute eye irritation has been assessed by means of the DRAIZE rabbit test, the limitations of which are known. Alternative tests based on in vitro models have been proposed. This work focuses on the "reconstituted human corneal epithelium" (R-HCE), which resembles the corneal epithelium of the human eye by thickness, morphology and marker expression. Testing a substance on R-HCE involves a variety of methods. Herewith quantitative morphological analysis is applied to optical microscope images of R-HCE cross sections resulting from exposure to benzalkonium chloride (BAK). The short term objectives and the first results are the analysis and classification of said images. Automated analysis relies on feature extraction by the spectrum-enhancement algorithm, which is made sensitive to
anisotropic morphology, and classification based on principal components analysis. The winning strategy has been the separate analysis of the apical and basal layers, which carry morphological information of different types. R-HCE specimens have been ranked by gross damage. The onset of early damage has been detected and an R-HCE specimen exposed to a low BAK dose has been singled out from the negative and positive control. These results provide a proof of principle for the automated classification of the specimens of interest on a purely morphological basis by means of the spectrum enhancement algorithm.
The Cell Transformation Assay (CTA) is one of the promising in vitro methods used to predict human carcinogenicity.
The neoplastic phenotype is monitored in suitable cells by the formation of foci and observed by light microscopy after
staining. Foci exhibit three types of morphological alterations: Type I, characterized by partially transformed cells, and
Types II and III considered to have undergone neoplastic transformation. Foci recognition and scoring have always been
carried visually by a trained human expert. In order to automatically classify foci images one needs to implement some
image understanding algorithm. Herewith, two such algorithms are described and compared by performance. The
supervised classifier (as described in previous articles) relies on principal components analysis embedded in a training
feedback loop to process the morphological descriptors extracted by "spectrum enhancement" (SE). The unsupervised
classifier architecture is based on the "partitioning around medoids" and is applied to image descriptors taken from
histogram moments (HM). Preliminary results suggest the inadequacy of the HMs as image descriptors as compared to
those from SE. A justification derived from elementary arguments of real analysis is provided in the Appendix.
The "enhanced spectrum" of an image g[.] is a function h[.] of wave-number u obtained by a sequence of operations on the power spectral density of g[.]. The main properties and the available theorems on the correspondence between spectrum enhancement and spatial differentiation, of either integer or fractional order, are stated. In order to apply the enhanced spectrum to image classification, one has to go, by interpolation, from h[.] to a polynomial q[.]. The graph of q[.] provides the set of morphological descriptors of the original image, suitable for submission to a multivariate statistical classifier. Since q[.] depends on an n-tuple, Ψ, of parameters which control image pre-processing, spectrum enhancement and interpolation, then one can train the classifier by tuning Ψ. In fact, classifier training is more articulated and relies on a "design", whereby different training sets are processed. The best performing n-tuple, Ψ*, is selected by maximizing a "design-wide" figure of merit. Next one can apply the trained classifier to recognize new images. A recent application to materials science is summarized.
Cell Transformation Assays (CTA) rely on the detection of phenotypic changes, namely foci, induced by chemicals (e.g.,
xenobiotics or candidate drugs) in mammalian cells such as C3H10T1/2 mouse fibroblasts. A focus is a cell colony and
as such is made visible by standardized techniques of light microscopy. Foci exhibit a variety of morphological features,
by which three "Types" have been defined. Types II and III consist of cells having undergone neoplastic transformation.
The assignment of a focus to a Type is based on the evaluation of phenotypic features by a trained human expert. An
automated, two-stage morphological classifier of foci is described herewith. Morphological descriptors are extracted
from light microscope images by the "spectrum enhancement" algorithm, which separates structure from texture. Said
descriptors are submitted to a classifier, the first stage of which is trained to discriminate transformed cells from normal
ones and the 2nd stage to discriminate Type III from Type II. The classifier operating in recognition mode (on images not
used for training) is satisfactory in terms of confusion matrix entries. The whole procedure is aimed at removing
subjectivity from the scoring and classification of foci and thus make CTA a more powerful tool in carcinogenesis
studies.
In order to evaluate the potential hematotoxicity of xenobiotics, including candidate anti-cancer drugs, in vitro models of hematopoiesis are used, which involve clonogenic assays on CFU-GM (Colony Forming Unit-Granulocyte-Macrophage). These assays require live and unstained colonies to be counted. Most laboratories still rely on visual scoring, which is time consuming and error prone. As a consequence automated scoring is highly desired. A classification algorithm aimed at emulating the colony recognition and scoring capabilities of a human expert has been developed. A first account will be given herewith. Assays were carried out on CFU-GM progenitors derived from human umbilical cord blood cells and grown in methylcellulose. A three-dimensional (3-D) medium is essential for these assays to simulate the clonogenetic process which takes place in bone marrow. Stacks of images representing slices of a 3-D domain were acquired. Structure and texture information was extracted from each image. Classifier training was based on a 3-D colony model applied to the image stack. The number of scored colonies (assigned class) was required to match the count supplied by the human expert (class of belonging). Successful applications to scoring colonies, which partially overlap and/or are masked by caustics, are described. Whereas the industry's scoring methods all rely on image structure alone and process 2-D data, the classifier described herewith takes texture into account and fuses 3-D dtat from a whole stack.
These authors have been developing for some years a variety of morphological classifiers, which analyse images, extract descriptors by FOURIER analysis, fractal analysis and spatial differentiation, fuse these descriptors by means of multivariate statistics. Classifiers have been trained, validated and applied to recognizing patterns belonging to new classes. One of the most relevant application has been the quantitative morphology of microtubule organisation. Results, which have been described in a number of publications, have consisted of: a) the quantitative assessment of structural damage caused by xenobiotics and the ensueing recovery, and b) the estimation of dose- and time- response relations. This paper, in addition to presenting a survey of the classification methods and the related results, will focus on some instructive class-wide and cell-wise statistical properties deduced from the first principal component only. These properties lead to three questions about the dose-response behaviour of microtubules which are still open.
A classifier capable of ranking structural alterations of the cytoskeleton is developed. Images of cytoskeletal microtubules obtained from the epifluorescence microscopy of primary culture rat hepatocytes are analyzed. Morphological descriptors are extracted by contour and mass fractal analysis, direct methods, and spectrum enhancement. All methods are designed and tuned to make the extracted morphological descriptors insensitive to absolute fluorescence intensities. Spectrum enhancement is a nonlinear filter that involves spatial differentiation of the gray-scale image followed by conversion of power spectral density to the logarithmic scale and averaging over arcs in the reciprocal domain. Enhanced spectra exhibit local maxima that correspond to the structured microtubule bundles of a normal cytoskeleton. Descriptor fusion for classification is achieved by means of multivariate analysis. The classifier is trained by image sets representing normal ("negative control") microtubules and those altered by exposure to a fungicide at the highest dose of the experiment design. Some sensitivity and validation tests, including discriminant functions analysis, are applied to the classifier. The latter is applied to recognize images of microtubules not used in the training stage and comes from treatments at lower concentrations and shorter times. As a result, structural alterations are ranked and structural recovery after treatment is quantified. The method has potential use in quantitative, morphology-based tests on the cytoskeleton treated either by anticancer drugs or by cytotoxic agents.
Airborne material particles in the 5μm size range have been collected, resuspended and analyzed by the TAOS (two-dimensional angular optical scattering) technique. The corresponding patterns of light intensity scattered by single particles have been automatically classified by an algorithm based on "spectrum enhancement", multivariate statistics and supervised optimization. The enhanced spectrum has resulted from some non-linear operations on fractional spatial derivatives of the pattern. It has yielded morphological descriptors of the pattern. A multiobjective optimization algorithm has included principal components analysis and has maximized pairwise discrimination between classes. The classifier has been trained by TAOS patterns from 10μm polystyrene spheres (P) and background aerosol particles (B). Then it has been applied to recognize patterns from airborne debris (A) sampled on a car racing track. Training with at least 10 patterns per class has discriminated P and B from A at confidence levels ≥90%. Training by samples of smaller sizes (e.g., 5P and 12B patterns) has obviously yielded lower confidence levels (65% in B-A discrimination).
The "enhanced spectrum" of an image g[.] is a function h[.] of wavenumber u obtained as follows. A reflection operation Q[.] is applied to g[.]; the power spectral density I G[u]2 of Q[g[.]] is converted to the Log scale and averaged over a suitable arc; the function s[.] of u alone is thus obtained, from which a known function, the "model" m[u], is subtracted: this yields h[u]. Models m(p)[.] used herewith have a roll-off like -1OLog10[uP]. As a consequence spectrum enhancement is a non-linear image filter which is shown to include partial spatial differentiation of Q[g[.]] of suitable order. The function h[.] emphasizes deviations of s[.] from the prescribed behaviour m(p)[.]. The enhanced spectrum is used herewith as the morphological descriptor of the image after polynomial interpolation. Multivariate statistical analysis of enhanced spectra by means of principal components analysis is applied with the objective of maximizing discrimination between classes of images. Recent applications to materials science, cell biology and environmental monitoring are reviewed.
Recently, these authors developed a heterogeneous, one-level image classifier (CH) based on morphological descriptors from direct domain analysis (spatial differentiation), fractal analysis and “spectrum enhancement” (a kind of non-linear filtering). Classifier CH was applied to epi-fluorescence microscope images of cytoskeletal microtubules and was trained to recognize structural alterations of the cytoskeleton in various circumstances. The application dealt with images of rat hepatocytes (rh). The scope of this paper is twofold: a) to investigate different classifier architectures, which include the multiobjective optimization of some image analysis parameters by means of suitable algorithms; b) to apply said classifiers to new sets of images obtained from mouse fibroblasts (mf) and HepG2 (hg) cells. Image sets from control and treated cell cultures are analyzed. Classifier CH is applied to mf microtubules. A new classifier entirely relying on “spectrum enhancement” (although on different descriptors) is developed and applied to rh and hg images. From the latter classifier, by bringing in descriptors from direct domain and fractal analysis, a hierarchical classifier is derived and applied to rh images. Results are compared. Classifier performance is expressed in terms of sensitivity, specificity and information contents of the first three principal components.
Aluminum silicate nanoaggregates grown at near-room temperature on an organic template under a variety of experimental conditions have been imaged by transmission electron microscopy. Images have been automatically classified by an algorithm based on “spectrum enhancement”, multivariate statistics and supervised optimization. Spectrum enhancement consists of subtracting, in the log scale, a known function of wavenumber from the angle averaged power spectral density of the image. Enhanced spectra of each image, after polynomial interpolation, have been regarded as morphological descriptors and as such submitted to principal components analysis nested with a multiobjective parameter optimization algorithm. The latter has maximized pairwise discrimination between classes of materials. The role of the organic template and of a reaction parameter on aggregate morphology has been assessed at two magnification scales. Classification results have also been related to crystal structure data derived from selected area electron diffraction patterns.
Direct methods (spatial differentiation), fractal analysis and spectral analysis (“spectrum enhancement”) have been applied to extract morphological descriptors from images of cytoskeletal microtubules. Images had been obtained from experiments on cultured cells (rat hepatocytes). Principal components analysis has been applied to morphological descriptors. An image classifier has thus been trained to tell normal (control) microtubule structures from those treated by a given concentration of a fungicide for a given time. Validation has been performed on sets of new images of the same two classes. Then the classifier has been used to rank the morphology of microtubules treated at lower doses and to quantify structural recovery after exposure. The paper is the first account of extensive morphological classification of microtubules and paves the way to a dose-response relationship based on quantitative morphology.
The morphology of cytoskeletal microtubules has been analyzed by fractal, direct and spectral methods. Sets of images were obtained from the epifluorescence microscopy of primary cultures of rat hepatocytes treated with fungicide concentrations of 5O and 25 µg/ml for 2h. The morphological descriptors extracted by said methods included contour and mass fractal dimension, total variation, the L1-norm of the Laplacian and properties of the "enhanced spectrum". The latter is obtained by suitably processing the logarithm of power spectral density with the aim of separating image structure (low spatial frequency) from texture (high spatial frequency). Descriptors were fused by principal components analysis. A classification algorithm was trained to tell undisturbed (control) cytoskeletal structures from those treated at the higher dose. The eigenvector matrix of the trained classifier was used to rank structures treated at the lower dose: from regression on the set centroid coordinates a tentative relation between the first principal component (the "response") and dose has been obtained. The same ranking procedure was applied to structures recovering from injury (24h after exposure to the higher dose) and the extent of recovery has been quantified. The paper includes a possible interpretation of some morphological descriptors and their role in automatic classification.
The cytoskeletal microtubules (MTs) of rat hepatocytes treated by Benomyl (a fungicide) were imaged by means of immunofluorescent staining and optical microscopy. Images of untreated, or control (C), and of treated (T) cells were processed both by fractal and Fourier analysis. The C-MTs had contour fractal dimensions higher (≥ 1.4) than those of T-MTs (≤1.3). Fourier analysis included computation of the anisotropy of power spectral density, angle averaging and "spectrum enhancement," which corresponds to the application of a (pseudo)differential operator to the image. Enhanced spectra were interpolated by a polynomial, q, of degree 39, from which morphological descriptors were extracted. Descriptors from Fourier analysis made image classification possible. Principal components analysis was applied to the descriptors. In the plane of the first two components, {z1,z2}, the minimum spanning tree was drawn. Images of T-MTs formed a single cluster, whereas images of C-MTs formed two clusters, C1 and C2. The component z1 correlated positively with the local maxima and minima of q, which reflected differences between T and C in power spectral density in the 1 to 2000 cycles/mm spatial frequency band. The difference between C1 and C2 was ascribed to anisotropy of the MT bundles. The implemented image classifier is capable of telling differences in cytoskeletal organization. As a consequence the method can become a tool for testing cytotoxicity and for extracting quantitative information about intracellular alterations of various origin.
The method presented is aimed at identifying the shape of an axially symmetric, sound soft acoustic scatterer from knowledge of the incident plane wave and of the scattering amplitude. The method relies on the approximate back propagation (ABP) of the estimated far field coefficients to the obstacle boundary and iteratively minimizes a boundary defect, without the addition of any penalty term. The ABP operator owes its structure to the properties of complete families of linearly independent solutions of Helmholtz equation. If the obstacle is known, as it happens in simulations, the theory also provides some independent means of predicting the performance of the ABP method. The ABP algorithm and the related computer code are outlined. Several reconstruction examples are considered, where noise is added to the estimated far field coefficients and other errors are deliberately introduced in the data. Many numerical and graphical results are provided.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.
